Oh, this is a fun way to do it! We should do a bunch of threads like this about different characters or issues. Anyway:
-- Why didn't OMT ever teach Jack a thing or go see him ride?
Because above all else, he was a jerk.
-- What did he know or suspect about Jack? How about Jack and Ennis? How about Jack and Randall?
He knew Jack was gay ("I know where Brokeback Mountain is") and that J & E were lovers. He knew there was another man in Jack's life, but he didn't know the guy's name. Someone recently said that it's very significant that Randall is never actually named by OMT (and that in fact the naming or not naming of characters is apparently significant throughout the story).
-- Was he a mean SOB through and through, or was he genuinely grieving Jack (not mutually exclusive, actually)?
Both.
-- Was he homophobic?
Not as far as we know. He says nothing that's unequivocally homophobic -- in fact (I know I've said this many times, but here goes again for the official record) doesn't seem to mind that Jack is planning to leave his wife and live with another man, only that he never carried out the plans and therefore didn't lick the ranch into shape. I'm not saying OMT should be elected president of the local PFLAG chapter. But his bitterness and anger just happen to be directed elsewhere, for whatever reason.
It would have been very easy for Annie Proulx and the filmmakers to have OMT something that indicated homophobia, or disapproval of Jack's sexuality. A single word or two inserted into his monologue would do it. For that matter, you would hardly expect him NOT to say something homophobic, given the culture and his age and so forth. But he doesn't, and I think that's not an accident. Especially in view of the way we're set up to assume he IS homophobic, that in fact that was the root of his conflicts with Jack. And it's such an interesting parallel and contrast with Ennis' dad, who Ennis usually speaks so well of that we're led to believe HE is an OK guy, until we find out he isn't.
If neither of Jack's parents are homophobic, it helps explain why Jack is fairly well adjusted about his sexuality. Because again Ennis, in contrast, is not well adjusted largely because of his own dad.
The whole story and movie are about people not always being what they seem or what you'd expect. A non-homophobic OMT would certainly fit that description.
-- Why didn't he let Ennis take the ashes?
Hmm ... Well, I really like the theory about denying Ennis the ashes as punishment for letting Jack down -- it would be poignant and kind of romantic. I don't totally buy it, though. I think mainly he just wanted to assert control and be a bastard. After all, if he were that concerned about his son, you'd think he'd at least see that his wishes was carried out, about the ashes I mean, even if it meant scattering them himself.
-- When he insisted Jack be buried in the "family plot," what did he mean -- was that an allusion to what we think of as (anti-gay) family values, or simply an assertion of control, or something else entirely?
IMO, this is the only thing OMT says that could be viewed as a sign of homophobia. "Family plot" carries an echo of "family values" and plot is a synonym for story -- suggesting that, in the end, he's forcing Jack to conform to society's rules, to be in the story involving a traditional family. And when he complains that Jack "thought he was too special," he could be saying he's become high-falutin since he got wealthy, or he could mean special as in atypical -- i.e., gay. So in other words, he could be saying "Jack thought that he could break society's rules by being gay." But in the end, he couldn't.
-- Ennis protectively shields the shirts when walking past OMT in the kitchen. What if he hadn't, and John Twist had seen the shirts? Would he have snatched them from Ennis' hands?
No, he wasn't up to any agression beyond the verbal. But part of the reason Ennis shelters them is not that he thinks OMT will overpower him and wrest them away, but just to keep them private and pure.
-- How does story-OMT differ from movie-OMT? Can you imagine movie-OMT participating in the peeing-on-Jack scene that was in the story but omitted from the movie?
The peeing scene is unfilmable and would have wrecked the emotional flow of that whole bedroom scene. But beyond that, movie-OMT is simply a more sympathetic character than story-OMT (just as movie-Mrs. Twist is a far more sympathetic character than story-Mrs. Twist).